aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours…

aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. two of his points are (3, 1.5) and (5, 2.5). which statement describes the slope of the line through these two points? it takes aaron about 1 hour to mow 2 acres. aarons rate for mowing lawns is 0.5 acres per hour. the ratio of acres to time is 5 acres to 3 hours. the rate to mow a lawn is 0.6 hours per acre.

aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. two of his points are (3, 1.5) and (5, 2.5). which statement describes the slope of the line through these two points? it takes aaron about 1 hour to mow 2 acres. aarons rate for mowing lawns is 0.5 acres per hour. the ratio of acres to time is 5 acres to 3 hours. the rate to mow a lawn is 0.6 hours per acre.

Answer

Explanation:

Step1: Calculate the rate of mowing

The rate of mowing is the change in area divided by the change in time. Given two points $(x_1,y_1)=(3,1.5)$ and $(x_2,y_2)=(5,2.5)$. The rate $r=\frac{y_2 - y_1}{x_2 - x_1}$. $r=\frac{2.5 - 1.5}{5 - 3}=\frac{1}{2}=0.5$ acres per hour.

Step2: Analyze each statement

  • For the statement "It takes Aaron about 1 hour to mow 2 acres": If the rate is 0.5 acres per hour, to mow 2 acres, the time $t=\frac{2}{0.5}=4$ hours, so this statement is false.
  • For the statement "Aaron's rate for mowing lawns is 0.5 acres per hour": We calculated the rate as 0.5 acres per hour, so this statement is true.
  • For the statement "The ratio of acres to time is 5 acres to 3 hours": The ratio based on our - calculated rate is 0.5 acres per hour, not 5 acres to 3 hours, so this statement is false.
  • For the statement "The rate to mow a lawn is 0.6 hours per acre": Since the rate is 0.5 acres per hour, the time per acre is $\frac{1}{0.5} = 2$ hours per acre, so this statement is false.

Answer:

Aaron's rate for mowing lawns is 0.5 acres per hour.